Answer:
the probability that a randomly selected officer who is female will be promoted is 0.051 or approximately 0.05.
Explanation:
a) To find the probability of being promoted or being female, we need to add the number of individuals who are promoted and the number of females, but subtract the number of individuals who are both promoted and female, as we do not want to count them twice. So, the probability of being promoted or being female is:
(Promoted + Female - Promoted and Female) / Total number of officers
= (288 + 36 - 36) / (288 + 36 + 672 + 204)
= 288 / 1200
= 0.24
Therefore, the probability of being promoted or being female is 0.24.
b) We need to find the probability of being promoted given that the randomly selected officer was female. This is a conditional probability, which can be found using the formula:
Probability of being promoted given that the officer is female = (Probability of being promoted and female) / (Probability of being female)
We are given the number of females who were promoted, which is 36. So the numerator is 36. The denominator is the number of females, which is 36, plus the number of males who were not promoted, which is 672. So, the denominator is 36 + 672 = 708.
Probability of being promoted given that the officer is female = 36 / 708
= 0.051
Therefore, the probability that a randomly selected officer who is female will be promoted is 0.051 or approximately 0.05.